88.12.24 problem 26

Internal problem ID [24080]
Book : Elementary Differential Equations. By Lee Roy Wilcox and Herbert J. Curtis. 1961 first edition. International texbook company. Scranton, Penn. USA. CAT number 61-15976
Section : Chapter 2. Differential equations of first order. Miscellaneous Exercises at page 55
Problem number : 26
Date solved : Thursday, October 02, 2025 at 09:57:31 PM
CAS classification : [[_2nd_order, _missing_y]]

\begin{align*} \sin \left (x \right ) y^{\prime \prime }&=y^{\prime } \end{align*}

✓ Maple. Time used: 0.001 (sec). Leaf size: 19

ode:=diff(diff(y(x),x),x)*sin(x) = diff(y(x),x); 
dsolve(ode,y(x), singsol=all);
 

\[ y = c_1 -\left (\ln \left (\sin \left (x \right )\right )+\ln \left (\csc \left (x \right )+\cot \left (x \right )\right )\right ) c_2 \]

✓ Mathematica. Time used: 0.118 (sec). Leaf size: 30

ode=D[y[x],{x,2}]*Sin[x]==D[y[x],x]; 
ic={}; 
DSolve[{ode,ic},y[x],x,IncludeSingularSolutions->True]
 

\begin{align*} y(x)&\to c_1 \sqrt {\sin ^2(x)} \csc (x) \log \left (\sec ^2\left (\frac {x}{2}\right )\right )+c_2 \end{align*}

✓ Sympy. Time used: 2.221 (sec). Leaf size: 24

from sympy import * 
x = symbols("x") 
y = Function("y") 
ode = Eq(sin(x)*Derivative(y(x), (x, 2)) - Derivative(y(x), x),0) 
ics = {} 
dsolve(ode,func=y(x),ics=ics)
 

\[ y{\left (x \right )} = C_{1} + C_{2} \int \frac {\sqrt {\cos {\left (x \right )} - 1}}{\sqrt {\cos {\left (x \right )} + 1}}\, dx \]